Question

In recent years, the number of people in a certain country who are 100 years old or older can be estimated by the function

p(t) = 1.32t − 2589.6
where
t = the year
p(t) = the number of people, in thousands, who are 100 or older.
(See Example 4.)
(a) Find p(2015)
p(2015) = thousand


Find p(2025)
p(2025) = thousand


(b) Use the function to estimate when the number of people 100 years or older will reach 100,000. (Round your answer to the nearest year.)

Answer 1

See below for answers

Explanation:

(a) Substitute t=2015 into the function:

p(t) = 1.32t - 2589.6

p(2015) = 1.32(2015) - 2589.6

p(2015) = 2659.8 - 2589.6

p(2015) = 70.2

So, there will be 70,200 people in 2015 who will be 100 years or older.

Substitute t=2025 into the function:

p(t) = 1.32t - 2589.6

p(2025) = 1.32(2025) - 2589.6

p(2025) = 2673 - 2589.6

p(2025) = 83.4

So, there will be 83,400 people in 2025 who will be 100 years or older.

(b) Substitute p(t)=100 into the function and solve for t:

p(t) = 1.32t - 2589.6

100 = 1.32t - 2589.6

2689.6 = 1.32t

2037.57 = t

2038 = t

Therefore, the number of people 100 years or older will reach 100,000 by 2038.